If $\mathrm{Pd} \mathrm{v}/\mathrm{s}. \mathrm{P}$ (where P denotes pressure in atm and d denotes density in $\mathrm{gm}/\mathrm{L}$ ) is plotted for ${\mathrm{H}}_2$ gas (ideal gas) at a particular temperature. If ${\left[\frac{\mathrm{d}}{\mathrm{dP}}\left(\mathrm{Pd}\right)\right]}_{\mathrm{P}=8.21 \mathrm{atm} }=10$, then the temperature will be:

A vessel of uniform cross-section of length $500$ as shown figure is divided in two parts by a weightless & frictionless piston one part contains $5$ moles of ${\mathrm{N}}_2\left(\mathrm{g}\right)$ and other part contains $2$ moles of ${\mathrm{H}}_2\left(\mathrm{g}\right)\&1$ mole of $\mathrm{He}\left(\mathrm{g}\right)$ gaseous mixture at the same temperature and pressure.

What is the length of ${\mathrm{N}}_2$ compartment?

(Assume volume of piston to be negligible)

In two different vessels $\mathrm{A}$ and $\mathrm{B}$ containing ${\mathrm{H}}_2\mathrm{O}\left(\ell \right)$ at the same temperature, the vacant space left over the surface of ${\mathrm{H}}_2\mathrm{O}\left(\ell \right)$ is $\mathrm{V}$ and $4 \mathrm{V}$. What is the ratio of $\left[(\mathrm{K}·\mathrm{E}{)}_{\mathrm{A}}/(\mathrm{K}·\mathrm{E}{)}_{\mathrm{B}}\right]$ of vapour's in two vessels?

What is the mass of ${\mathrm{H}}_2\mathrm{O}$ present in air in $10$ litre closed vessel with $80\%$ relative humidity at $1 \mathrm{atm}$ and $300 \mathrm{K}$ ?

Given: Vapour pressure of ${\mathrm{H}}_2\mathrm{O}$ is $30$ torr at $300 \mathrm{K}$.

Berthelot proposed the following empirical relation to explain the real behaviour of the real gases :

$\left(\mathrm{P}+\frac{\mathrm{a}}{{\mathrm{TV}}^2}\right)(\mathrm{V}-\mathrm{b})=\mathrm{RT}$

If the Berthelot equation of state be one of the forms of virial equation for 1 mole real gas is as under:

$\mathrm{PV}=\mathrm{RT}\left[1+\frac{\mathrm{A}}{\mathrm{V}}+\frac{\mathrm{B}}{{\mathrm{V}}^2}+\frac{\mathrm{C}}{{\mathrm{V}}^3}+\dots . \mathrm{to} \mathrm{higher} \mathrm{powe} \mathrm{rof} \mathrm{n}\right]$

where A, B and C are constants which are known as second, third and fourth virial coefficients respectively. Then what will be the correct value of Boyle's temperature i.e., ${\mathrm{T}}_{\mathrm{B}}$ i.e., the temperature at which $\mathrm{PV}=\mathrm{RT}$ i.e., ideal gas equation is obeyed?